Question

18. Assuming the correlation of stock A & B is zero (which your book assumes for all securities), Portfolio A,B’s total risk is closest to:

1. 9.4%

2. 10.2%

3. 11.1%

4. 12.8%

5. 13.2%

   Assume the risk free rate is 2.0%. The SP500 is considered the market. Today (T-0), you invest $400 in Stock A and $600 in Stock B to create Portfolio A,B. Assume there are not taxes or dividends. The one year performance of the stocks and the market is summarized in the table below. Use this information to help answer questions 16-20. Total Return 12.0% 18.0% 10.0% Total Risk 14,0% 15.0% 12.0% Investment Beta Market Stock A Stock B 1.00 400 600 0.60 16. Portfolio A,B's beta is closest to: a. 0.80 b. 0.92 c. 1.00 d. 1.08 e. 1.20

Answer 1

Answer to Question 16:

We have the information relating to stock beta and investment in each stock. With these information, we can calculate beta of portfolio A,B.

Stocks	Investment	Weight (wi) #	Beta ( βi)	Weight * Beta (wi βi)
Stock A	400	0.4	1.4	0.56
Stock B	600	0.6	0.6	0.36
Total	1000	1.0		0.92

Note: ^# The weights are arrived by dividing investment in stock by total investment. Stock A - (400/1000)   Stock B - (600/1000)

Therefore, the portfolio Beta is 0.92.

Answer to Question 18:

As per Markowitz's portfolio theory, formula for portfolio variance is =

σ_p²= (w₁² * σ₁² ) + (w₂² * σ₂² ) + 2 w₁ w₂ COV₁₂

W = weight , σ² = variance and COV₁₂ is the covariance between stock 1 and stock 2.

COV₁₂ = r * σ₁ * σ₂    where, r is the co-efficient of correlation

It is given in the question that, correlation between stocks is zero. Hence, the value of COV₁₂ is also zero.

therefore, calculation of portfolio variance as per above formula is as below:

= [(0.4)² * (15)²] + [(0.6)² * (12)²] + 2 * 0.4 * 0.6 * 0

= 36 + 51.84 + 0

σ_p² = 87.84

Portfolio risk is the square root of portfolio variance.

Therefore, square root of 87.84 is the portfolio risk.

= 9.372 i.e., 9.4%